the top tail of the wealth distribution in germany, france, spain, …€¦ · forbes and national...
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The Top Tail of the Wealth Distribution
in Germany, France, Spain, and Greece
Stefan Bach, Andreas Thiemann, Aline Zucco
Global Economic Symposium, 2015
Kiel, October 13, 2015
Outline
Background and motivation
Data
HFCS
Forbes and national rich lists
Estimation and imputation of the top wealth distribution
Results for the adjusted top wealth concentration
Discussion Paper:
Stefan Bach, Andreas Thiemann, Aline Zucco: The Top Tail of the Wealth Distribution in Germany,
France, Spain, and Greece. DIW Berlin Discussion Papers 1502, 2015.
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Background and motivation
Rising inequality in income and wealth, in particular at the top
Poor information on the top tail of household wealth
Household surveys
• German Socio-Economic Panel (SOEP), 2002, 2007, 2012
• Household Finance and Consumption Survey (HFCS) 2009-11
• Underrepresentation of top income and wealth
– Sampling error (“non observation bias“)
– Selectivity (“non response bias“, “middle class bias“)
Administrative data
• Wealth and estate taxation: Selectivity due to tax rules
• Family owned firms, foundations, family offices: Non-disclosure
Rich lists of the big fortunes: Forbes World’s billionaires, national rich lists
National and financial accounts: macro aggregates
Estimation of top wealth concentration in Germany, France, Spain, and Greece
Integration of HFCS and rich lists
Estimation of Pareto distribution for the top tail
• following Vermeulen (2014)
Imputation of the missing rich
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Pareto distribution
Good approximation of the top tail of income and wealth
Pareto (1896), Kuznetzs (1955), Piketty & Saez (2003)
Based on two parameters (Representation in appendix)
Minimum wealth and „Pareto-alpha“
Net Household Wealth (HFCS Definition)
Total household assets (excluding pension wealth)
- Total outstanding household’s liabilities
= Household net wealth
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Conclusion
Top wealth concentration in Germany, France, Spain, and Greece
Underrepresentation in household surveys
Integration of the big fortunes from rich lists
• broader base of national rich lists compared with Forbes
Imputation of the missing rich by Pareto distribution
Adjustment substantially increases top wealth concentration
Top percentile share increases
• from 24 to 33 percent in Germany
• from 18 to 21 percent in France
• from 15 to 17 percent in Spain
• (from 8 to 12 percent in Greece)
National rich lists instead of Forbes increase top wealth concentration
• especially in France and Spain
Research perspectives
Data quality: Surveys and rich lists
Tax files from wealth taxes, estate taxes, financial statements of firms and foundations
Microsimulation analyses of wealth taxation
Distribution analyses of household wealth and income
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Thank You for Your Attention!
Back-up slides
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Pareto distribution
Idea and representation
Top wealth distribution follows a power-law function
• for any wealth wi that exceeds a threshold wmin, specified by the Pareto coefficient α
Density function
𝑓 𝑤𝑖 =
𝛼𝑤𝑚𝑖𝑛𝛼
𝑤𝑖𝛼+1 𝑖𝑓 𝑤𝑖 ≥ 𝑤𝑚𝑖𝑛
0 𝑖𝑓 𝑤𝑖 < 𝑤𝑚𝑖𝑛
(1)
Distribution function
𝑃 𝑊 ≤ 𝑤𝑖 = 𝐹 𝑤𝑖 = 𝑓 𝑡 𝑑𝑡 = 1 − (𝑤𝑚𝑖𝑛
𝑤𝑖)𝛼
𝑤
𝑤𝑚𝑖𝑛; ∀ 𝑤𝑖 ≥ 𝑤𝑚𝑖𝑛 (2)
Complementary cumulative distribution function (ccdf)
𝑃 𝑊 > 𝑤𝑖 = 1 − 𝑃 𝑊 ≤ 𝑤𝑖 = (𝑤𝑚𝑖𝑛
𝑤𝑖)𝛼; ∀ 𝑤𝑖≥ 𝑤𝑚𝑖𝑛 (3)
Interpreted as ranking (“Zipf's law”, Zipf/zeta distribution)
𝑛 𝑤𝑖
𝑛≅ (
𝑤𝑚𝑖𝑛
𝑤𝑖)𝛼; ∀ 𝑤𝑖≥ 𝑤𝑚𝑖𝑛 (4)
𝑙𝑛𝑛 𝑤𝑖
𝑛= −𝛼 ln
𝑤𝑖
𝑤𝑚𝑖𝑛 (5)
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Pareto distribution: Density and distribution function, complementary cumulative distribution function (ccdf)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
f(x),
F(x
), 1
-F
(x)
Net wealth in million Euro
f(x)
F(x)
α = 1
α = 2
1 - F(x)(ccdf)
α = 2
α = 1
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